The solar zenith angle dependence of desert albedo - Boston ...

GEOPHYSICAL RESEARCH LETTERS, VOL. 32, L05403, doi:10.1029/2004GL021835, 2005The solar zenith angle dependence of desert albedoZhuo Wang, Michael Barlage, and Xubin ZengInstitute of Atmospheric Physics, University of Arizona, Tucson, Arizona, USARobert E. DickinsonSchool of Earth and Atmospheric Sciences, Georgia Institute of Technology, Atlanta, Georgia, USACrystal B. SchaafDepartment of Geography, Boston University, Boston, Massachusetts, USAReceived 25 October 2004; revised 7 January 2005; accepted 8 February 2005; published 8 March 2005.[1] Most land models assume that the bare soil albedo is afunction of soil color and moisture but independent of solarzenith angle (SZA). However, analyses of the ModerateResolution Imaging Spectroradiometer (MODIS)Bidirectional Reflectance Distribution Function (BRDF)and albedo data over thirty desert locations indicate thatbare soil albedo does vary with SZA. This is furtherconfirmed using the in situ data. In particular, bare soilalbedo normalized by its value at 60° SZA can beadequately represented by a one-parameter formulation(1 + C)/(1 + 2C * cos(SZA)) or a two-parameter formulation(1 + B 1 *f 1 (SZA) + B 2 *f 2 (SZA)). Using the MODIS andin situ data, the empirical parameters C, B 1 , and B 2 aretaken as 0.15, 0.346 and 0.063. The SZA dependenceof soil albedo is also found to significantly affect themodeling of land surface energy balance over a desert site.Citation: Wang, Z., M. Barlage, X. Zeng, R. E. Dickinson, andC. B. Schaaf (2005), The solar zenith angle dependence of desertalbedo, Geophys. Res. Lett., 32, L05403, doi:10.1029/2004GL021835.1. Introduction[2] Land surface albedo is an important factor in climatemodeling, because it regulates the shortwave radiationabsorbed by the surface. Surface albedo depends on soilcharacteristics and vegetation types. Error in the specificationof soil albedo may cause biases in the computation ofground temperature and surface fluxes. In most land surfacemodels (LSMs), the bare soil albedo is assumed to be afunction of soil color and soil moisture but independent ofsolar zenith angle (SZA). Furthermore, most LSMs assumea uniform albedo over most desert areas.[3] Satellite data have convincingly shown the significantgeographic variation of desert albedo [Tsvetsinskaya et al.,2002; Wang et al., 2004], and they can be directly used inLSMs to address the uniformity assumption above. Remotesensing data from the satellite and aircraft platforms as wellas field measurements have also shown the anistropy of baresoil surfaces, because soils have relatively opaque verticalstructures that cause dark shadows [Kimes, 1983]. Forinstance, Monteith and Szeice [1961] showed that themeasured bare soil albedo increases from 0.16 at 30° SZAto 0.19 at 70° SZA with a daily mean of 0.17. Idso et al.Copyright 2005 by the American Geophysical Union.0094-8276/05/2004GL021835$05.00[1975] found that, on average, the curves of albedo asa function of the SZA for wet and dry conditions areidentical in shape. Ranson et al. [1991] compared thealbedo computed from two integration methods with simultaneouslyacquired in situ data. The albedo obtained for thebare soil also increases for sun angles away from solarnoon. The purpose of this study is to develop two simpleformulations to represent the SZA dependence of bare soilalbedo for weather and climate models and for the remotesensing retrieval of surface solar fluxes.2. Data Analysis[4] The global 0.05° Moderate-Resolution ImagingSpectroradiometer (MODIS) bidirectional reflectance distributionfunction (BRDF) and albedo Climate Modeling Grid(CMG) data (Version 4) are used in this study. The underlying1-km BRDF/albedo data were derived by coupling allavailable cloud-free, atmospherically corrected, spectralsurface reflectance observations over a 16-day period witha semi-empirical, kernel-driven BRDF model [Schaaf et al.,2002]. The MODIS data are provided in three visible (460,555, and 659 nm) and four near-infrared narrow bands (865,1240, 1640, and 2130 nm), which are then used to infer thetotal shortwave (SW, 0.3–5.0 mm), visible (VIS, 0.3–0.7 mm), and near-infrared (NIR, 0.7–5.0 mm) broadbandblack-sky (or direct) and white-sky (or diffuse) albedos.These data are reprojected and averaged to a 0.05° grid, andthe presence of snow and the quality of the majority of theBRDF inversions are stored for each gridbox. Only the dataderived primarily from full inversion under snow-freecondition are used. Furthermore, we analyze all of theBRDF data available from 2000 to 2004. Based on MODISLand Cover Type (MOD12) and Fractional VegetationCover dataset derived from MODIS NDVI data, we haveidentified thirty 0.05° pixels over different desert areas withzero fractional vegetation cover to examine the SZA dependenceof bare soil albedo. These pixels are selected torepresent each of the major deserts of the world and theirexact locations are available from the lead author.[5] At each pixel, the black-sky albedo and its SZAdependence do not change much during all the 16-dayperiods. For instance, for the albedo at 60° SZA over apixel (25.975°N, 5.075°E) in Africa, the interquartile ranges(IQRs); i.e., the differences between the 25th and 75thpercentiles, are 0.013 and 0.010 for the VIS and NIR bands,respectively. Since the soil moisture effect on surface albedoL054031of4

L05403 WANG ET AL.: SZA DEPENDENCE OF DESERT ALBEDO L05403Figure 1. The median curves of the MODIS black-skyalbedos in (a) VIS band and (b) NIR band versus the cosineof SZA at 30 desert locations. The normalized curves withrespect to their albedo values at 60° SZA are shown in(c) VIS band and (d) NIR band.would be minimal over this desert location, these smallvariations in black-sky albedo are probably primarily causedby the uncertainty of MODIS data themselves, although insome places, there may be a subpixel vegetation contributionas well. For each location, there is a median albedo amongall the 16-day periods at each SZA, so a curve can beobtained from median albedos over all SZAs. Figures 1aand 1b show these median SZA dependence curves of blackskyalbedo over all thirty pixels. The significant geographicvariation of desert albedo is consistent with previous studies[Tsvetsinskaya et al., 2002; Wang et al., 2004]. For instance,the IQRs of the black-sky albedos at 60° SZA are 0.065 and0.116 in the VIS and NIR bands, respectively. To see theSZA dependence more clearly, we normalize each curve inFigures 1a and 1b by its value at 60° SZA, and results areshown in Figures 1c and 1d. While the albedo increases withSZA over each pixel, its variation with SZA is quantitativelydifferent over different pixels.[6] The SZA dependence of the MODIS surface albedohas been evaluated using field measurements which includea desert site at the Surface Radiation Budget Network. Acase study over three stations reveals that the MODISBRDF model is able to capture the SZA dependence ofsurface albedo as shown by the field measurements [Jin etal., 2003]. Complementary to this study, here additional insitu data are used to further evaluate the MODIS data. Weuse the 0.05° (5 km) MODIS data to compare withheritage field measurements collected at a single location.Figure 2a compares the MODIS data with surface measurementsover a plowed field in Tunisia, Africa in April 1983[Pinty et al., 1989]. MODIS black-sky albedos are muchhigher than surface observations in both the VIS and NIRbands, possibly because of different surface conditions(including soil moisture) in April between 1983 and 2001and because of the inherent difference between a pointmeasurement and satellite measurements in a 0.05° grid.These differences are also contributed, to a lesser degree, bythe comparison of the MODIS black-sky albedo with the insitu measurements of true albedo that is a weighted averageof direct and diffuse albedos. To better compare the SZAdependence, we normalize each curve in Figure 2a by itsalbedo at 60° SZA in Figure 2b. Evidently, both MODIS andin situ albedos increase with SZA and their SZA dependencesare consistent with each other. Figures 2c and 2dcompare MODIS data with the in situ data over an Avondaleloam soil site in Phoenix, Arizona in May, July, September,and December 1973 [Idso et al., 1975]. Over dry or wet soil,the observed in situ albedo minimum occurred near thesmallest SZA at solar noon, while its maximum occurredat the greatest SZA in the morning and afternoon. TheMODIS black-sky albedo and its SZA dependence in theSW band (i.e., the spectrally weighted average of VIS andNIR bands) agree with the in situ measurements over drysoil. Figures 2e and 2f compare the in situ albedo measurementsof the tiger-bush soil over the Sahel desert in Marchand September 1990 [Allen et al., 1994] with the MODISSW albedos in 2001. It is unclear why the in situ albedo overwet soil actually decreases slightly with the increase of SZAfor SZA greater than 60°. The in situ albedos over dry soil lielargely between the MODIS albedos in March and September2001. However, the MODIS albedo increases faster withSZA than indicated by the in situ data.3. Two Simple Formulations for the SZADependence of Bare Soil Albedo[7] To adequately describe the SZA dependence of baresoil albedo as given in Figures 1 and 2, a new albedoFigure 2. Comparison of MODIS data with in situmeasurements. (a) The bare soil albedo in VIS and NIRbands versus cosine SZA in Tunisia, Africa in April 1983[Pinty et al., 1989]; (b) Same as (a) except for normalizedblack-sky albedos with respect to the albedo at 60° SZA;(c) The bare soil albedo in the SW band in Phoenix, Arizonain May, July, September, and December 1973 [Idso et al.,1975]; (d) Same as (c) except for normalized black-skyalbedos; (e) The bare soil albedo in the SW band over theSahel desert in March and September 1990 [Allen et al.,1994]; (f) Same as (e) except for normalized black-skyalbedos.2of4

L05403 WANG ET AL.: SZA DEPENDENCE OF DESERT ALBEDO L05403formulation is derived here using the MODIS BRDF/albedoalgorithm and data [Schaaf et al., 2002]:aq ðÞ¼a r f1þ B 1 bg 1 ðÞ qg 1 ð60 Þcþ B 2 bg 2 ðÞ qg 2 ð60 Þcgð1Þwhere a is the black-sky albedo, q is solar zenith angle, a r isthe albedo at 60° SZA and depends on season and location.The functions g 1 and g 2 are from the MODIS algorithm:g 1 ðÞ¼ q 0:007574 0:070987q 2 þ 0:307588q 3 andg 2 ðÞ¼ q 1:284909 0:166314q 2 þ 0:04184q 3 :The parameters B 1 and B 2 are the average of the ratios ofthe volumetric and geometric parameters in the MODISalgorithm [Schaaf et al., 2002] over a r for 30 pixels,respectively. Figures 3a–3d shows these parameters in VISand NIR bands for thirty pixels as a function of a r . Based onthis figure, we obtain B 1 = 0.346 and B 2 = 0.063.[8] We have also tested the simple formulation [Brieglebet al., 1986]:1 þ Caq ðÞ¼a r 1 þ 2C cos qwhere the empirical parameter C was taken as 0.4 for arablegrass, grassland and desert, and 0.1 for all other types[Briegleb et al., 1986]. Equation (2) and the above valuesfor C have also been used in the remote sensing retrieval ofland surface solar fluxes [Pinker and Laszlo, 1992] and insome land-atmosphere coupled models [e.g., Hou et al.,2002].[9] A more appropriate value for C can be determined byfitting each curve in Figures 1a and 1b to (2) by minimizingthe integral over all SZA’s for each 16-day period:V ¼ 2Z p=2q¼0ð2Þcos q sin q ða M a C Þ 2 dq ð3Þwhere a M is the MODIS albedo and a c is computed from(2). The weighting factor of cosq is the same as that used forcomputing the white-sky albedo [Schaaf et al., 2002]. Thisis chosen also because MODIS data are more reliable atSZA less than 70° and because the albedo is more importantat a smaller SZA when solar flux itself is large. The valuesfor C over all thirty pixels are plotted as a function of a r inFigures 3e and 3f. Their mean values for the VIS and NIRbands are 0.17 and 0.13, respectively, and their average of0.15 is used for both bands to be consistent with Briegleb etal. [1986]. Furthermore, the best-fit linear equations can beobtained: C VIS (a r ) = 0.29 0.51a r and C NIR (a r ) = 0.130.02a r . To compare the performance of (1) and (2), weP 1compute d = 30 1=2 , where V i is computed from (3)30V ii¼1for each of the 30 pixels. The values of d are 0.0061,0.0081, and 0.0072 using the two-parameter model, oneparametermodel with constant C as well as the best-fitlinear equations, respectively. This shows that the twoparametermodel is a little better than the one-parameterFigure 3. The median B 1 versus the MODIS black-skyalbedos at 60° SZA (a r ) for 30 pixels in (a) VIS band and(b) NIR band. The median B 2 versus a r in (c) VIS band and(d) NIR band. The values for C versus a r in (e) VIS bandand (f) NIR band (solid line: the best-fit linear function;dotted line: the average C value of VIS and NIR bands).(g) The SZA dependence at a pixel (19.975°N, 43.325°E)using the MODIS data directly and computed using (1) and(2) with different C (the best-fit linear function or fixedvalues) in the VIS band; (h) Same as (g) except in the NIRband.model. If the white-sky albedo is used (i.e., withoutconsidering the SZA dependence), the d value would be0.0195 and is much bigger than those using (1) or (2). Thisindicates the importance of the SZA dependence. Figures 3gand 3h evaluates the SZA dependence over a pixel(19.975°N, 43.325°E) using (1) and (2) with differentvalues for C. The simulated SZA dependence using the twoparameter,one-parameter model with the best-fit linearequation or the C fixed at 0.15 are consistent with theMODIS data for SZA less than 60°. In contrast, the albedocomputed with C = 0.4 increases with SZA much faster thanindicated by the MODIS data, and its value at zero SZA islower by 0.03 for the VIR band and 0.05 for the NIR band.[10] We have further evaluated the impact of the prescribedparameters C, B 1 , and B 2 on the computed SZAdependence using the in situ data in Figure 2e. It is foundthat the deviations of the simulated albedo using (1) or (2)with C = 0.15 from in situ data are much smaller than thosewith C = 0.4 for SZA less than 70° (figure not shown).Based on these analyses, we recommend the use of thepolynomial (1) or (2) with C = 0.15 over bare soil in landmodeling and remote sensing retrieval of land surfacesolar fluxes. Then the white-sky albedo can be obtainedanalytically by integrating (1) and (2) over all SZA’s [using3of4

L05403 WANG ET AL.: SZA DEPENDENCE OF DESERT ALBEDO L05403transferred into the soil (Figure 4c). The remaining energy isprimarily used to increase the ground temperature (Figure 4d)and is emitted as longwave radiation. Compared with CTL,the ground temperature at local solar noon is higher by 0.7°C,0.4°C, and 0.3°C in the RAD, NEW, and POL simulations,respectively (Figure 4d). There are systematic temperaturebiases in all four simulations in comparison with observations(Figure 4d), but it goes beyond the scope of this study tofurther address this issue. Additional observational data fromtwo sites in Arizona lead to similar conclusions.[13] In summary, our analyses of the MODIS and in situdata indicate that bare soil albedo depends on the SZA, andthis dependence can be adequately represented by (1) withB 1 = 0.346 and B 2 = 0.063 as well as (2) with C = 0.15.These dependences need to be considered in land modeling.Further work is also needed to evaluate the impact of theseformulations on the remote sensing retrieval of land surfacesolar fluxes.Figure 4. The sensitivity of the Noah land model to theSZA dependence of the bare soil albedo at a Sahel site.(a) Absorbed solar radiation difference between threedifferent simulations and CTL; (b) Sensible heat fluxdifference; (c) Ground heat flux difference; and (d) Groundtemperature bias of simulations from observations. See thetext for the meaning of each simulation.the weighting factor in (3)], and is a ws = 0.97a r for (1) anda ws = 0.96a r for (2).4. Impact of the SZA Dependence of SoilAlbedo on Land Modeling[11] We have incorporated (1) and (2) into the Noah landsurface model [Mitchell et al., 2004]. The model is forcedusing observations over a tiger bush site from the HydrologicAtmospheric Pilot Experiment in the Sahel [Goutorbeet al., 1997]. We run the model from Aug. 20 to Sept. 30,1992. The sensitivity of the Noah model to the SZAdependence of the albedo is shown in Figure 4. Foursimulations are completed. The observed monthly averagedalbedos for Aug., Sept., and Oct. are interpolated into theaverage daily albedo for these four runs. The controlsimulation (CTL) has no SZA dependence, similar to theoffline Noah model setup. Equation (1) is used to define aSZA dependence (B 1 = 0.346, B 2 = 0.063) in the POL run.The NEW run uses (2) with C = 0.15. The RAD simulationis also done using (2) with C = 0.4, as implemented inthe atmospheric radiative transfer scheme in the NCEP landatmospherecoupled model [Hou et al., 2002].[12] Figure 4 shows the 5-day averaged diurnal cycle forthe last 5 days of Sept. 1992. Compared with CTL, the SZAdependence formulations in (1) and (2) increase albedo atlarge SZA and decrease albedo at small SZA. Therefore, theabsorbed solar radiation (Figure 4a) behaves as expected,with increases at solar noon of about 38, 20, and 16 W/m 2 forthe RAD, NEW, and POL simulations, respectively. Sinceless solar radiation is incident at low sun angles, the SZAdependence does not affect the simulations much at sunriseand sunset. About 76% of the extra solar energy goes into anincrease in sensible heat flux (Figure 4b) while another 18% is[14] Acknowledgment. This work was supported by NASA undergrant NNG04GL25G and through its EOS IDS Program (429-81-22; 428-81-22), and by NOAA under grant NA03NES4400013.ReferencesAllen, S. J., J. S. Wallance, J. H. C. Gash, and M. V. K. Sivakumar (1994),Measurements of albedo variation over natural vegetation in the Sahel,Int. J. Remote Sens., 14, 625–636.Briegleb, B. P., P. Minnis, V. Ramanathan, and E. Harrison (1986),Comparison of regional clear sky albedos inferred from satellite observationsand model calculations, J. Clim. Appl. Meteorol., 25, 214–226.Goutorbe, J. P., et al. (1997), An overview of HAPEX-Sahel: A study inclimate and desertification, J. Hrdrol., 188–189, 4 – 17.Hou, Y. T., S. Moorthi, and K. Campana (2002), Parameterization of solarradiation transfer in the NCEP models, NCEP Off. Note 441, 34 pp., Natl.Cent. for Environ. Predict., Camp Springs, Md.Idso,S.B.,R.D.Jackson,R.J.Reginato,B.A.Kimball,andF.S.Nakayama (1975), The dependence of bare soil albedo on soil watercontent, J. Appl. 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Dickinson, School of Earth and Atmospheric Sciences, GeorgiaInstitute of Technology, Atlanta, GA 30332–0340, USA.C. B. Schaaf, Department of Geography, Boston University, Boston,MA 02215, USA.4of4